Rate of change of volume, in cubic centimeters per minute, =

Question

The radius of a spherical balloon is increasing at a rate of 2 centimeters per minute. How fast is the volume changing, in cubic centimeters per minute, when the radius is 8 centimeters?

Note: The volume of a sphere is given by: V=(4/3)pir^3

Answer 1

It is given dr/dt = 2 cm/min. When the radius is 8 cm, the volume rate is

dV/dt = 4πr² dr/dt = 4π(8 cm)² (2 cm/min) = 512π cm³